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  • lfunc_lfunctions • Show schema
    {'Lhash': '4341265815032813862625566863741', 'a10': [-0.8895767418546578, -0.368474751247869], 'a2': [0.6808525618501878, 0.6808525618501878], 'a3': [-1.0137182468642587, -2.447332340004771], 'a4': [0.0, -1.0728795780440725], 'a5': [-0.9238795325112867, 0.3826834323650898], 'a6': [0.9760798280192513, -2.3564651587628744], 'a7': [2.8590636293477, 1.1842629309634611], 'a8': [2.092177932968431, -2.092177932968431], 'a9': [-2.8404905548480377, 2.8404905548480377], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6787284171808836, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0.9238795325112867, -0.3826834323650898]]], [17, [[1.0, 0], [-1.2580404220379682, 3.926491346802961]]]], 'bad_primes': [5, 17], 'central_character': '85.66', 'coefficient_field': 'CDF', 'conductor': 85, 'conductor_radical': 85, 'conjugate': '2231019734958796020777475455241', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.6808525618501878, 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-1.2123530078266138, -1.1303203448426462], 'positive_zeros': ['3.42465488065181914391997182381130', '4.48111923211612207638936495719772', '5.48127203637532832781796205064102', '7.81049110404248174468690449369490', '8.811215207407080942777835111778786', '10.61312727147919754163920145926555', '11.08583476200567583409284123998041', '11.85632119275467760944128780947799', '13.34387287413421838893300974090361', '14.31975840917048058449574331718732'], 'prelabel': '2-85-17.15-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8238497540091176, 'root_angle': 0.12393748115918918, 'root_number': '0.7118116354830465 + 0.7023704119557931*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.123937481159', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.42465488065181914391997182381', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.48111923211612207638936495720', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.48127203637532832781796205064', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 0.6787284171808836, 'bad_primes': [5, 17], 'central_character': '17.15', 'conductor': 85, 'conductor_radical': 85, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/85/2/l/a/66/4'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-85-17.15-c1-0-4', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-85-17.15-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8238497540091176, 'root_angle': 0.12393748115918918, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.42465488065181914391997182381', 'prec': 103}}
  • lfunc_instances • Show schema
    {'Lhash': '4341265815032813862625566863741', 'Lhash_array': ['4341265815032813862625566863741'], 'factors': ['2-85-17.15-c1-0-4'], 'label': '2-85-17.15-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/85/2/l/a/66/4'}